In tomographic imaging, penetrating waves are used to gather projection data from an object under study from multiple directions. Different tomographic imaging modalities exist for different types of penetrating waves, for example, computed tomography generally refers to X-ray tomography, single-photon emission computed tomography and positron emission tomography refer to gamma ray tomography, magnetic resonance imaging uses radiofrequent waves, and other modalities exist for visible light, electron waves and ultrasound.
In the case of computed tomography, internal structure of a patient or object may be examined non-invasively. This typically involves the collection of projection data using a detector which performs measurements relating to x-ray beams cast through the patient or object from various angles by a moving x-ray source. This allows to calculate the distribution of beam attenuation properties inside the patient or object, for example in the single plane of rotation of the moving x-ray source, or even such a distribution in a 3D volume, for example by combining a source rotating in a plane with a translation of the object of patient in a direction perpendicular to this plane.
The reconstruction of a spatial representation, e.g. a planar image or a 3D image volume, from such projection data, may be achieved by using algorithms known in the art. Most reconstruction algorithms can be subdivided in two classes: analytical reconstruction techniques, e.g. variants of filtered backprojection (FBP), and iterative algebraic methods, such as Algebraic Reconstruction Technique (ART), Simultaneous Algebraic Reconstruction Technique (SART) or Simultaneous Iterative Reconstruction Technique (SIRT). Furthermore, hybrid reconstruction methods are known in the art. Such methods may combine both types of reconstruction algorithms, for example by using an FBP reconstruction as the initial solution for an algebraic method.
Filtered backprojection is a high-performance analytical reconstruction technique, and yields accurate results when a large number of projections are available, data is acquired with a high signal-to-noise ratio (SNR) and a full 180° angular range is covered by the projections. This technique is characterized by the two operations, filtering and backprojection, e.g. performing a discrete inverse Radon transform. Backprojection involves the redistribution of projection data values over points along the corresponding projection lines in space, while filtering involves weighting the projection data to counteract blurring of the backprojected image. The applied filtering, for example as defined by a convolution kernel, therefore determines the image quality of an image reconstruction to a great extent. The ideal convolution kernel depends on the specific imaging methodology, and may only be determined analytically in idealized situations, e.g. neglecting discretization effects, projections obtained by rotation along a circular path involving a fixed angular step size and covering a full rotation.
Alternatively, tomographic reconstruction may be carried out using algebraic reconstruction algorithms, such as the well-known ART, SIRT or similar algorithms. These methods do not depend on filters, and therefore circumvent difficulties in determining suitable filters for filtered backprojection in complex imaging geometries. These algorithms may typically involve iteratively adjusting an image to minimize a difference metric between simulated projection data for this image and the measured projection data. Algebraic reconstruction methods may be considered more flexible in dealing with limited data problems and noise compared to filtered backprojection. They may furthermore allow for incorporation of certain types of prior knowledge, e.g. constraints such as non-negativity of the reconstructed image, by adjusting the image between subsequent iterations. Unfortunately, the iterative nature of these methods renders them computationally more intensive.
In the patent specification U.S. Pat. No. 7,447,295 B2, a method is disclosed for providing filters for use in filtered backprojection, which are specifically attuned to a predetermined scanning geometry. This method involves using an algebraic reconstruction algorithm, e.g. ART, in calculating a filter. Particularly, this method uses projection data obtained for a test object, e.g. a thin wire or other object with preferably a broad spatial frequency bandwidth, to calculate a filter for application in filtered backprojection. Alternatively to obtaining projection data by actually imaging a test object, this tomographic imaging may be simulated.